Tomasz Kania

collaborators

14 papers

math.FA2026

Pointwise function spaces over compacta are not weak Banach spaces

Tomasz Kania, Jerzy Kąkol

Let $K$ be a compact Hausdorff space and let $E$ be an infinite-dimensional real Banach space. We prove that there is no continuous bijection $h : C_{p} (K) \to E_{w}$ whose inverse…

math.GN2026

Talagrand compacta, 2DCP, and pointwise quotients

Tomasz Kania, Jerzy KÄ kol

We revisit Talagrand's CH compactum as a test object for the two-disjoint-copies property and for pointwise quotient questions. The two-disjoint-copies property, or 2DCP, is a topo…

math.FA2026

Amenability constants for unconditional sums of Banach algebras

Tomasz Kania, Jerzy KÄ kol

We study Johnson amenability for unconditional direct sums of Banach algebras. Given a family $(A_{i})_{i \in I}$ of Banach algebras and a Banach sequence lattice $E$ on~ $I$ , the $E$ -…

math.LO2026

Polish spaces for countable and separable structures through quotient encodings

Tomasz Kania

We develop a quotient-based framework for locating natural properties of countable algebraic structures and separable Banach-type structures in the Borel hierarchy. The common idea…

math.FA2026

Uniform Property (S)

William B. Johnson, Tomasz Kania

We introduce and investigate a quantitative version of Steinhaus' property $(S)$ for Banach spaces, called the \emph{uniform property $(S)$ }. A Banach space $X$ is said to have unifor…

math.CA2026

Parallelepipeds of maximal facet area and total edge length in ellipsoids, through prescribed boundary points

Tomasz Kania

Let \[ \mathcal{E}_A=\{x\in\mathbb{R}^n:x^{\top}A^{-1}x\le 1\},\qquad n\ge2, \] where $A$ is real symmetric positive definite. We study full-dimensional parallelepipeds whose $2^{n}$ …